Problem 67 Evaluate each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 67

Evaluate each expression. $$ \frac{-2-5}{-7+(-7)} $$

Short Answer

Expert verified

The expression evaluates to $\frac{1}{2}$.

Step by step solution

Simplify the Numerator

We start by simplifying the numerator of the expression $-2 - 5$.$-2 - 5 = -7$. Thus, the numerator simplifies to $-7$.

Simplify the Denominator

Next, we simplify the denominator of the expression $-7 + (-7)$. This is the same as $-7 - 7 = -14$. Thus, the denominator simplifies to $-14$.

Divide Numerator by Denominator

Now, we divide the simplified numerator by the simplified denominator to evaluate the expression:$\frac{-7}{-14}$. Dividing $-7$ by $-14$ gives us $\frac{1}{2}$, because a negative divided by a negative results in a positive value.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator Simplification

Simplifying the numerator is the first step to making any fraction simpler. In the context of the given exercise, the numerator begins with an expression $-2 - 5$. When handling negative numbers, remember that subtracting makes the values more negative. Thus, $-2$ minus $5$ becomes $-7$. To simplify the numerator:

Identify all terms present in the numerator.
Apply basic arithmetic operations, taking note of positive and negative signs.

In our example, we only needed to consider two numbers, which made simplification straightforward. Once complete, your numerator will be ready for the next step in fraction simplification.

Denominator Simplification

Next, you must simplify the denominator. In this exercise, the denominator consists of the expression $-7 + (-7)$. Adding two negative numbers is like subtracting their absolute values from zero. Since both numbers are $-7$, combining them gives $-14$.Steps to simplify the denominator:

Recognize all components in the denominator.
Combine similar terms while respecting their signs (positive or negative).

In practice, attend to the signs carefully. They determine the arithmetic action you'll take: addition or subtraction. Simplifying the denominator ensures the fraction is set for final computation.

Division of Integers

The final crucial step is dividing the simplified numerator by the simplified denominator. In your fraction, both the numerator and the denominator are negative: $\frac{-7}{-14}$. Dividing two negative numbers entails that the resulting quotient becomes positive. Hence, $-7$ divided by $-14$ results in $\frac{1}{2}$.For dividing integers:

Identify the signs. If both integers share the same sign, the result is positive.
If the signs differ, the result is negative.

Always simplify the resulting fraction if possible, though in this particular problem, $\frac{1}{2}$ is already in its simplest form. This process wraps up the simplification of a fraction involving division of integers.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Evaluate each expression. $$ \frac{-2-5}{-7+(-7)} $$

Short Answer

Step by step solution

Simplify the Numerator

Simplify the Denominator

Divide Numerator by Denominator

Key Concepts

Numerator Simplification

Denominator Simplification

Division of Integers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Geometry

Applied Mathematics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.